Coexistence and bistability of a modified Leslie–Gower predator–prey model with mixed movement for the predator and Holling-type II schemes

Abstract

This paper centers on the analysis of the dynamics of a modified Leslie–Gower predator–prey model employing Holling-type II schemes, with the prey exhibiting pure random diffusion and the predator undergoing a mixed form of movement. The extinction of species and uniform persistence of this system are explored, and several conditions for the stability, uniqueness and multiplicity of positive steady-state solutions are derived. In contrast to the specialist and generalist predator–prey systems in open advective environments, the dynamics of this system are more intricate. It emerges that multiple positive steady-state solutions and the bistable phenomenon exist for this system when a small advection rate and a moderate predation rate are imposed. Numerical simulations reveal that the increase of diffusion rate for prey disadvantages the survival of itself and has no impact on predator invasion, while the increase of diffusion rate for predators favors the invasion of itself.